A car (m = 1510 kg) is parked on a road that rises 12.6 ° above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?
Wc = m*g = 1510kg * 9.8N/kg = 14,798 N.
= Wt. of car.
Fc = 14,798N @ 12.6o = Force of car.
Fp = 14798*sin12.6 = 3228 N. = Force
parallel to hill.
a. Fv = 14,798*cos12.6 = 14,442 N.=Force
perpendicular to hill or Normal.
b. Fp-Fs = ma.
3228-Fs = m*a = m*0 = 0.
Fs = 3228 N. = Force of static friction.
To find the magnitudes of the normal force and the static frictional force that the ground exerts on the tires of a parked car on an inclined road, we will need to consider the forces acting on the car.
1. Start by drawing a free-body diagram of the car. Identify the forces acting on it:
a) The gravitational force (weight) acting vertically downwards with a magnitude of mg, where m is the mass of the car (1510 kg) and g is the acceleration due to gravity (9.8 m/s^2).
b) The normal force (N) acting perpendicular to the incline.
c) The static frictional force (f_s) acting parallel to the incline. Note that the static frictional force prevents the car from sliding down the incline.
2. Resolve the weight force into components:
The weight force can be resolved into two components: one that acts parallel to the incline (mg*sinθ) and one that acts perpendicular to the incline (mg*cosθ), where θ is the angle of the incline (12.6°).
3. Determine the normal force (N):
The normal force (N) is the vertical force exerted by the ground on the car, perpendicular to the incline. Since the car is at rest, the normal force must balance the vertical component of the weight. Therefore, N = mg*cosθ.
4. Calculate the static frictional force (f_s):
The static frictional force (f_s) is the force that prevents the car from sliding down the incline. It acts parallel to the incline and opposes any tendency of the car to move. Since the car is stationary, the magnitude of the static frictional force can be calculated using the equation f_s ≤ μ_s * N, where μ_s is the coefficient of static friction.
5. Substitute the known values into the formulas:
a) To find the normal force (N): N = mg*cosθ.
b) To calculate the static frictional force (f_s): f_s ≤ μ_s * N.
Note: The coefficient of static friction (μ_s) depends on the surfaces in contact. If it is not given, you will need additional information to determine it.
6. Solve the equations:
Substitute the values of m, g, θ, and μ_s into the formulas obtained in the previous steps to find the magnitudes of the normal force (N) and static frictional force (f_s).